Ilya ZaliapinDepartment of Mathematics and Statistics

University of Nevada, Reno

SAMSI workshop “Dynamics of Seismicity”Thursday, October 10, 2013

Yehuda Ben-ZionDepartment of Earth Sciences

University of Southern California

Spatio-temporal evolution of seismic clusters in southern and central California

Earthquake clusters: existence, detection, stability

Clusters in southern California

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Outline

o Main types of clusterso Topological cluster characterization

Evolution of clustering with relation to large events44

Cluster type vs. physical properties of the lithosphere

Data

•Southern California catalog: Hauksson, Yang, Shearer (2012) available from SCEC data center; 111,981 earthquakes with m ≥ 2

•Heat flow data from www.smu.edu/geothermal

Baiesi and Paczuski, PRE, 69, 066106 (2004)Zaliapin et al., PRL, 101, 018501 (2008)

Zaliapin and Ben-Zion, GJI, 185, 1288–1304 (2011)Zaliapin and Ben-Zion, JGR, 118, 2847-2864 (2013)Zaliapin and Ben-Zion, JGR, 118, 2865-2877 (2013)

10 , 0ibmdr

(Fractal) dimension of epicenters

Intercurrence time Spatial distance Gutenberg-Richter law

[M. Baiesi and M. Paczuski, PRE, 69, 066106 (2004)]

/2 /2Rescaled time 10 , Rescaled distance 10i ibm bmdT R r

[Zaliapin et al., PRL, 101, 018501 (2008)]

, log log logTR T R

Distance from an earthquake j to an earlier earthquake i :

Definition:

Property:

Separation of clustered and background parts in southern California

Earthquake jPa

rent (n

eares

t neig

hbor)

i

Zaliapin and Ben-Zion, JGR (2012)Zaliapin et al., PRL

(2008)

Background and clustered parts in models

Zaliapin and Ben-Zion, JGR (2013)Zaliapin et al., PRL

(2008)

Homogeneous Poisson process ETAS model

Separation of clustered and background parts in southern CaliforniaBackground = weak links

(as in stationary, inhomogeneous Poisson

process)

Clustered part = strong links (events are much closer to each

other than in the background part)

Zaliapin and Ben-Zion, JGR (2013)Zaliapin et al., PRL

(2008)

weak linkstrong link

Cluster #3

Cluster #2

Cluster #1

Identification of clusters: data driven

Time

Foreshocks

Aftershocks

Mainshock

Identification of event types: problem driven

Time

Single

ETAS declustering: Example

29,671 events

9,536 mainshocks

① Burst-like clusters Represent brittle fracture. Large b-value (b=1), small number of events,

small proportion of foreshocks, short duration, small area, isotropic spatial distribution.

Tend to occur in regions with low heat flow, non-enhanced fluid content, relatively large depth => increased effective viscosity.

② Swarm-like clusters Represent brittle-ductile fracture. Small b-value (b=0.6), large number of

events, large proportion of foreshocks, long duration, large area, anisotropic channel-like spatial pattern.

Tend to occur in regions with high heat flow, increased fluid content, relatively shallow depth => decreased effective viscosity.

③ Singles Highly numerous in all regions; some but not all are related to catalog

resolution.

④ Clusters of the largest events Most prominent clusters; object of the standard cluster studies. Not

representative of the majority of clusters (mixture of types 1-2).

M5.75

M5.51

M5.51 M5.75

L= 417, tree depth = 9, ave. depth = 3.8 L= 572, tree depth = 44, ave. depth = 30.3

Swarm vs. burst like clusters:Topologic representation

Burst-like Swarm-like

Tim

e

Tim

e

Average leaf depth (number of generations from a leaf to the root):Bimodal structure

HYS (2012), mM ≥ 2

Large topological depth:Swarm-like clusters

Small topological depth:Burst-like clusters

ETAS model

Heat flow in southern Californiahttp://www.smu.edu/geothermal

Preferred spatial location of burst/swarm like clusters 195 clusters with m ≥ 4, N ≥ 10; spatial average within 50 km

Moment of foreshocks relative to that of mainshock 195 clusters with m ≥ 4, N ≥ 10; spatial average within 50 km

Family size 112 Δ- clusters with m ≥ 4, N ≥ 10; spatial average within 50 km

X-zone

X-zone

D-zone

D-zone

Time

Spa

ce

N-zone

Statistical analysis of premonitory patterns: zero-level approach

D = 2 years, X = 1 year, R = 200 km, M=6.5mainshocks with m>3 are examined

All mainshocks

Topological depth (average leaf depth)

Δ = X = 3 years, R = 100km m > 3, N > 20

ANOVA p =7x10-7 : Significant difference

Large families, N > 20

Topological depth (average leaf depth)

Δ = X = 2 years, R = 100km m > 3

All mainshocks

Proportion of families

Δ = X = 2 years, R = 100km m > 3, N >1

Families (N > 1)

Proportion of large families (N>=5)

Large earthquakes in California, M6.5

2) Landers, M7.3, 1992

4) Hector Mine, M7.1, 1999

1) Superstition Hills, M6.6, 1987

5) El Mayor Cucapah, M7.2, 2010

3) Northridge, M6.7, 1994

L

EMCL

“San Jacinto Fault”

SH

EMC

LN

HM

Families with 3 < m < 4

Families with size L > 10

“San Jacinto Fault”

SH EMC

L N HM

Topological depth d > 6, mainshock m< 5

100 km from Superstition Hills, M6.6 of 1987

SH EMCL N HM

Salton Trough

Average leaf depth > 1, Family size > 5

SH EMCL N HM

Salton Trough

Baja California

Average leaf depth > 1, Family size > 5

Baja California

SH EMCL N HM

Average leaf depth > 1, Family size > 5

R < 5 km

R < 20 km

R < 100 km

R < 300 km

El Mayor Cucapah, M7.2

Topological depth d > 5

20 km from Landers, M7.3 of 1992

In this region: 613 mainshocks; 139 families; 11 mainshocks/10 families with m>3.5

Remote aftershock of Superstition Hill, M6.6 of 1987

Landers, M7.3 of 1992

Remote foreshock to Hector Mine, M7.1 of 1999

SH EMCL N HM

Seismic clusters in southern California1

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Summary

o Four types of clusters:• Burst-like clusters• Swarm-like clusters• Singles• Largest regional clusters

o Topological cluster characterization

o Swarm-like clusters <-> decreased effective viscosityo Burst-like clusters <-> increased effective viscosity

Spatial variability: Relation to physical properties of the crust

Temporal variability: Relation to large events